Senate Majority Leader Mitch McConnell said it could take weeks to reach an agreement, though House Majority Leader Kevin McCarthy was more optimistic.

"Both sides can sit down, find a compromise that actually secures the border. We had everybody in the room say they want a secure border. So maybe we work a combination to make it solved," McCarthy said.

Senate Minority Leader Chuck Schumer floated the idea of reopening the government while the two sides continue to hash out border security.

"Open up the government, as we continue to debate what is the best way to secure our borders," he said.

But earlier today, Trump said he's willing to keep the partial shutdown going.

"As long as it takes. I mean, look, I'm prepared. I think the people of the country think I'm right," Trump said.

Democrats are expected to vote on that spending package after they assume control of the House on Thursday, even though the Republican-controlled Senate has said it won't rubber stamp anything the president doesn't approve of.